Our notions of things are never simply commensurate with the things themselves; they are aspects of them, more or less exact, and sometimes a mistake _ab initio_. Take an instance from arithmetic:—We are accustomed to subject all that exists to numeration; but, to be correct, we are bound first to reduce to some level of possible comparison the things which we wish to number. We must be able to say, not only that they are ten, twenty, or a hundred, but so many definite somethings. For instance, we could not without extravagance throw together Napoleon’s brain, ambition, hand, soul, smile, height, and age at Marengo, and say that there were seven of them, though there are seven words; nor will it even be enough to content ourselves with what may be called a negative level, viz. that these seven were an un-English or are a departed seven. Unless numeration is to issue in nonsense, it must be conducted on conditions. This being the case, there are, for what we know, collections of beings, to whom the notion of number cannot be attached, except _catachrestically_, because, taken individually, no positive point of real agreement can be found between them, by which to call them. If indeed we can denote them by a plural noun, then we can measure that plurality; but if they agree in nothing, they cannot agree in bearing a common name, and to say that they amount to a thousand these or those, is not to number them, but to count up a certain number of names or words which we have written down.